JEE Main 2024MathematicsVector AlgebraMediumMCQ

JEE Main 2024 — Vector Algebra Question with Solution

JEE Main 2024 (29 Jan Shift 2)

Question

Let OA→=a→,OB→=12a→+4b→ and OC→=b→, where O is the origin. If S is the parallelogram with adjacent sides OA and OC, then area of the quadrilateral OABCarea of S is equal to _____

Choose an option

Show full solutionCorrect option: D
Correct answer
D8

Step-by-step explanation

Area of parallelogram, S=|a→×b→|

Area of quadrilateral = Area ∆OAB+Area ∆OBC

=12{|a→×(12a→+4b→)|+|b→×(12a→+4b→)|}

=12{|4a→×b→|+|12b→×a→|}

=12{4|a→×b→|+12|a→×b→|}

=162|a→×b→|

=8|(a→×b→)|

Ratio =8|(a→×b→)||(a→×b→)|=8

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About this question

This is a previous-year question from JEE Main 2024, covering the Vector Algebra chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.